Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.
Identification of Nonlinear Discrete Systems From Probability Density Sequences.IEEE Transactions on Circuits and Systems I: Regular Papers, 70(2):846–859
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On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data
Diffeomorphisms and vector fields are uniquely identifiable from finitely many pushforward densities or weighted divergences, with the number of required observations determined by embedding theorems.